Following the mild solution theory of fractional/normal evolution equations in
[1]}, [2]}, [3]}, [4]}, we introduce the following mild
solutions. Assume that \( 0 < \alpha \leqslant 1 \)  and \( 0 < T < \infty \) . For
any
\(g \in L^1(0,T;[X^*,Y]_\theta ) \quad \text{with}\quad 0 \leqslant \theta \leqslant 1,\) 
